Physics quiz question: sound system capacitor

Physics 205B Quiz 4, fall semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 17.73(b)

"C22_MAIN.JPG"
Sound System Laboratories
soundstormlab.com/auto/car-audio-sound-system-auto-stereo-capacitor-farad-sound-storm-c22/

A Sound Storm Laboratories C22 car audio system capacitor[*] stores 400 J of energy when it holds 40 C of charge. The potential difference across the capacitor is:
(A) 5.0 V.
(B) 10 V.
(C) 20 V.
(D) 8.0×10³ V.

[*] soundstormlab.com/auto/car-audio-sound-system-auto-stereo-capacitor-farad-sound-storm-c22/.

Correct answer (highlight to unhide): (C)

The electric potential energy in a capacitor is given by EPE = (1/2)·Q·∆V, such that:

∆V = 2·EPE/Q = 2·(400 J)/(40 C) = 20 J/C = 20 V.

(Response (A) is (1/2)·(EPE/Q); response (B) is EPE/Q; response (C) is (1/2)·EPE·Q.)

Student responses
Section 70856
(A) : 0 students
(B) : 4 students
(C) : 7 students
(D) : 0 students

Success level: 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42